Because type 1 diabetes tends to develop earlier in life than type 2 diabetes, and because the public is repeatedly told that type 2 diabetes is a result of poor lifestyle choices, most people, including most type 1 diabetics I have met, believe that type 1 diabetes is genetic or at least more genetic than type 2 diabetes.
Now, whether something is "more genetic" is something I realize is hard to define. Having a family member with type 2 diabetes puts you at a higher risk of diabetes than a family member with type 1... but then again, being a human being puts you at a higher risk of type 2 diabetes than type 1.
Having a family member with type 1 diabetes multiplies your risk of getting type 1 diabetes by many times more than having a family member with type 2 diabetes does... but that's in no small part because, with 1 in 3 members of my generation expected to develop type 2 diabetes in our lives, you can't possibly multiply that risk by more than 3.
A few forms of diabetes that are entirely genetic exist. They include some forms of neonatal diabetes, the various MODY diabetes, and diabetes associated with certain genetic disorders such as cystic fibrosis (in which the pancreatic ducts clog up).
But your run of the mill type 1 and type 2 diabetes are an interaction between environment and genetics. According to the ADA the genetic component of type 2 diabetes is larger. Having a family member with type 2 diabetes puts you at a higher diabetes risk than having a family member with type 1 diabetes does.
The ADA page contains stuff that is mathematically impossible though. It claims that the risk of a child developing type 1 is 1-6% if a parent has it; but that 1 in 7 type 1s have a particular gene and if they do have that gene, the kid has a 1 in 2 chance of type 1 diabetes. Well, 1/2 time 1/7 is 1/14 which is more than 6%. I don't buy it. For one thing, as far as I can tell, that gene does not exist. Polyglandular autoimmune syndrome 2 (which basically means having multiple auotimmune endocrine disorders, particularly thyroid disease and type 1 diabetes) has not been shown to be caused by any one gene.
I was going to write a lot about HLA types but I'm too tired. Let me say instead that the fact that fascinates me most about diabetes and genetics is that having a different high risk allele from each parent- being heterozygous- confers the highest diabetes risk.